Estimation of static strength of adhesively bonded single lap joints with an acrylic adhesive under tensile shear condition based on cohesive zone model

In this study, the tensile shear and bending tests of adhesively bonded single lap joints with the acrylic adhesive was evaluated experimentally and numerically. In the previous paper, the traction-separation laws in mode 1 and mode 2 for an acrylic adhesive were directly obtained from the observation of failure process using Arcan type adhesively bonded specimens: simultaneous measurements of the J-integral and the opening displacements in the directions normal, δ_n and tangential to the adhesive layer, δ_s respectively. The experimental results were compared with numerical simulations conducted in ABAQUS including cohesive damage model. The cohesive laws obtained in the previous paper were simplified to trapezoidal shape from the experimentally obtained ones which were indicated in the previous paper. A good agreement was found between the experimental and numerical results. Then, to investigate the damage evolution in the adhesive layer for some lap joints, microscopic video observation was conducted near the end of the adhesive layer, and the video image have been compared with the contours of damage variable obtained by FEM corresponding to the video images. The observed damage evolution also agrees with the trend of damage variable.     

Strength prediction of adhesively bonded joints under cyclic thermal loading using a cohesive zone model

Structural adhesives are being widely adopted in aerospace and automobile industries. However, in many cases, hostile environments cause non-ignorable degradation in joints mechanical performance. In this work, a combined experimental–numerical approach was developed to characterise the effect of cyclic-temperature environment on adhesively bonded joints. The environmental degradation factor, Deg, was introduced into a cohesive zone model to evaluate the degradation process in the adhesive layer caused by the cyclic-temperature environment and the stress states in adhesive layer before and after temperature exposure treatment were investigated. Carefully designed experimental tests were carried out to validate the simulation results and help the numerical procedure to predict joint mechanical behaviour after environmental exposure. A response surface method was utilised to provide a better visualisation on the relationship between selected factors and response. Finally, the scanning electron microscopy was carried out to investigate the micro fracture mechanisms of adhesively bonded joints.     

Predicting the strength of adhesively bonded joints of variable thickness using a cohesive element approach

One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker–Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.     

Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method

Adhesives have become the method of choice for many structural joining applications. Therefore, there is a need for improved understanding of adhesive joint performance, especially their failure, under a variety of loading conditions. Various numerical methods have been proposed to predict the failure of adhesive bonded material systems. These methods generally use a cohesive zone model (CZM) to analyze crack initiation and failure loci. The CZM incorporates a traction–separation law which relates the jump in surface tractions with the jump in displacements of abutting nodes of the cohesive segment; the area under the curve relating these jumps equals the energy release rate which is determined from experimental data. Values of parameters in the CZM are usually obtained through the comparison of results of numerical simulations with the experimental data for pure mode I and mode II deformations. Here a numerical approach to simulate crack initiation and propagation has been developed by implementing CZM in the meshless method using the symmetric smoothed particle hydrodynamics (SSPH) basis functions, and using the design of experiments technique to find optimal values of CZM parameters for mode I failure. Unlike in the finite element method where a crack generally follows a path between element boundaries, in the meshless method a crack can follow the path dictated by the physics of the problem. The numerical technique has been used to study the initiation and propagation of a crack in a double cantilever beam under mode I and mixed mode in-plane loadings. Computed results are found to agree well with the corresponding experimental findings. Significant contributions of the work include the determination of optimum values of CZM parameters, and simulating mode I, mode II and mixed mode failures using a meshless method with the SSPH basis functions.     

Comparison of cohesive zone and continuum damage approach in predicting the static failure of adhesively bonded single lap joints

The paper presents a comparison of the cohesive zone model (CZM) and the continuum damage mechanics approach in predicting the static failure of a single lap joint (SLJ). The effect of mesh size and viscosity were studied to give more understanding on the failure load and computational time. Both the load–displacement response and the backface strain technique were utilised to compare the validity of predictions. Peel and shear stress and damage distributions along with the damage progression are compared to understand the behaviour of the models in predicting the static failure response. In general, both approaches show good accuracy in predicting the failure load; however, the cohesive zone approach requires shorter computation time than the continuum damage approach. The continuum damage approach shows some mesh-dependency particularly for elements with high aspect ratios, whereas the cohesive zone approach is not. The continuum damage approach is less sensitive than the cohesive zone approach to the artificial damping required to achieve convergence. Another interesting finding is using the same ultimate stress level of damage in the continuum damage approach at the peak load is much lower than that in the cohesive approach; but the failure process in this approach is faster.     

Progressive damage modeling of adhesively bonded lap joints

A continuum damage model for simulating damage propagation of bonded joints is presented, introducing a linear softening damage process for the adhesive agent. Material models simulating anisotropic non-linear elastic behavior and distributed damage accumulation were used for the composite adherends as well. The proposed modeling procedure was applied to a series of lap joints accounting for adhesion either by means of secondary bonding or co-bonding. Stress analysis was performed using plane strain elements of a commercial finite element code allowing implementation of user defined constitutive equations. Numerical results for the different overlap lengths under investigation were in good agreement with experimental data in terms of joint strength and overall structural behavior.     

Behavior and failure of adhesive bonds in pin fin heat sinks using cohesive zone model

Adhesive bonding is a versatile material joining method that tends to distribute the load over the bonded area and provide more flexibility in selecting the base material without worrying about the joining process and its effects. To improve the performance of heat sinks, polymer composite pin fin are used to improve the thermal conductivity. Adhesives are usually used in bonding composite fins to their metal base plate. In this work we provide a methodology for estimating the fatigue life of the adhesive joint. A thermo-mechanical cohesive zone model (CZM) is used at the interfaces to measure the softening of the bond under thermal cyclic loading which in turn decreases the critical stress for failure. A summary of the fatigue crack initiation (FCI) life prediction model is presented before a qualitative study is performed to estimate the effect of convection environment on the life and behavior of the adhesive bond.     

Accuracy of cohesive laws with different shape for the shear behaviour prediction of bonded joints

The use of adhesive bonding as a joining technique is increasingly being used in many industries because of its convenience and high efficiency. Cohesive Zone Models (CZM) are a powerful tool for the strength prediction of bonded joints, but they require an accurate estimation of the tensile and shear cohesive laws of the adhesive layer. This work evaluated the shear fracture toughness (J_IIC) and CZM laws of bonded joints for three adhesives with distinct ductility. The End-Notched Flexure (ENF) test geometry was used. The experimental work consisted of the shear fracture characterization of the bond by the J-integral. Additionally, by this technique, the precise shape of the cohesive law was defined. For the J-integral, digital image correlation was used for the evaluation of the adhesive layer shear displacement at the crack tip during the test, coupled to a Matlab sub-routine for extraction of this parameter automatically. Finite Element Method (FEM) simulations were carried out in Abaqus® to assess the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the ENF tests. As output of this work, fracture data is provided in shear for the selected adhesives, allowing the subsequent strength prediction of bonded joints.     

Strength prediction of adhesively bonded carbon/epoxy joints

A finite element approach has been used to obtain the stress distribution in some adhesive joints. In the past, a strength prediction method has not been established. Therefore in this study, a strength prediction method for adhesive joints has been examined. First, the critical stress distribution of single-lap adhesive joints, with six different adherend thicknesses, was examined to obtain the failure criteria. It was thought that the point stress criterion, which has been previously used for an FRP tensile specimen with a hole, was effective. The proposed method using the point stress criterion was applied to adhesive joints, such as single-lap joints with short non-lap lengths and bending specimens of single-lap joints. Good agreement was obtained between the predicted and experimental joint strengths.     

Numerical design and multi-objective optimisation of novel adhesively bonded joints employing interlocking surface morphology

A novel concept for joining materials is presented which employs adhesive joints with interlocking bond-surface morphology formed on the surfaces of male and female adherends that mechanically interlock in shear when brought together. In the present work, miniature, single-lap joint specimens with a single truncated square pyramid interlocking profile, centred in the bond area, are investigated. The performance of the concept is assessed through finite element analysis (FEA) by incorporating yield criteria representing plasticity in the adherends and a cohesive zone model to represent damage in the adhesive layer. This allows for effective simulation of the joint response until ultimate failure and thus, full assessment of the concept's performance. Various interlocking geometries are explored and refined through an adaptive surrogate modelling design optimisation procedure coupled with FEA. The results indicated that significant improvements in work to failure, of up to 86.5%, can be achieved through the more progressive failure behaviour observed compared to that of a traditional adhesively bonded joint. Improvements in the joint's ultimate failure load can also be achieved with a relatively ductile adhesive system.     

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.     

Low-speed bending impact behavior of adhesively bonded single-lap joints

This study addresses the low-speed impact behavior of adhesively bonded single-lap joints. An explicit dynamic finite element analysis was conducted in order to determine the damage initiation and propagation in the adhesive layers of adhesive single-lap joints under a bending impact load. A cohesive zone model was implemented to predict probable failure initiation and propagation along adhesive–adherend interfaces whereas an elasto-plastic material model was used for the adhesive zone between upper and lower adhesive interfaces as well as the adherends. The effect of the plastic deformation ability of adherend material on the damage mechanism of the adhesive layer was also studied for two aluminum materials Al 2024-T3 and Al 5754-0 having different strength and plastic deformation ability. The effects of impact energy (3 and 11 J) and the overlap length (25 and 40 mm) were also investigated. The predicted contact force-time, contact force-central displacement variations, the damage initiation and propagation mechanism were verified with experimental ones. The SEM and macroscope photographs of the adhesive fracture surfaces were similar to those of the explicit dynamic finite element analysis.     

Simulation of adhesive joints using the superimposed finite element method and a cohesive zone model

Adhesive joints have been widely used in various fields because they are lighter than mechanical joints and show a more uniform stress distribution if compared with traditional joining techniques. Also they are appropriate to be used with composite materials. Therefore, several studies were performed for the simulation of the bonded joints mechanical behavior. In general for adhesive joints, there is a scale difference between the adhesive and the substrate in geometry. Thus, mesh generation for an analysis is difficult and a manual mesh technique is needed. This task is not efficient and sometimes some errors can be introduced. Also, element quality gets worse.In this paper, the superimposed finite element method is introduced to overcome this problem. The superimposed finite element method is one of the local mesh refinement methods. In this method, a fine mesh is generated by overlaying the patch of the local mesh on the existing mesh called the global mesh. Thus, re-meshing is not required.Elements in the substrate are generated. Then, the local refinement using the superimposed finite element method is performed near the interface between the substrate and the adhesive layer considering the shape of the element, the element size of the adhesive layer and the quality of the generated elements. After performing the local refinement, cohesive elements are generated automatically using the interface nodes. Consequently, a manual meshing process is not required and a fine mesh is generated in the adhesive layer without the need for any re-meshing process. Thus, the total mesh generation time is reduced and the element quality is improved. The proposed method is applied to several examples.     

Failure analysis of AA8011-pultruded GFRP adhesively bonded similar and dissimilar joints

In this work, a comparative failure analysis of aluminum (AA8011/AA8011) and glass fiber reinforced polyester (GFRP/GFRP) based similar and dissimilar joints is presented. The GFRP is prepared using pultrusion technique. Single lap joints are prepared by using Araldite R2011 epoxy as an adhesive. The lap joints are then tested under tension to estimate the average shear strength of the assembly. It is observed that the average bond strength of AA8011/AA8011 is lesser than that of the GFRP/GFRP joint. The failure of similar joints occurred by fracture within the adhesive. The dissimilar joint is failed predominantly by interface debonding. Further, a detailed three dimensional stress analysis of the joints is carried out using finite element method (FEM). The damage analysis of adhesive layer is carried out by coupling FEM with cohesive zone model (CZM). The stress, damage distributions and failure mechanisms are compared for similar joints in detail. A failure mechanism is proposed for AA8011/AA8011 type joint that favours a rapid crack growth in the adhesive after crack initiation, which is responsible for lesser bond strength. The increase in overlap length has positive effect that the peak load increases proportionally with overlap length.     

Predicting environmental degradation of adhesive joints using a cohesive zone finite element model based on accelerated fracture tests

A framework was developed to predict the fracture toughness of degraded adhesive joints by incorporating a cohesive zone finite element (FE) model with fracture data of accelerated aging tests. The developed framework addresses two major issues in the fracture toughness prediction of degraded joints by significant reduction of exposure time using open-faced technique and by the ability to incorporate the spatial variation of degradation with the aid of a 3D FE model. A cohesive zone model with triangular traction-separation law was adapted to model the adhesive layer. The degraded cohesive parameters were determined using the relationship between the fracture toughness, from open-faced DCB (ODCB) specimens, and an exposure index (EI), the time integration of the water concentration. Degraded fracture toughness predictions were done by calculating the EI values and thereby the degraded cohesive parameters across the width of the closed joints. The framework was validated by comparing the FE predictions against the fracture experiment results of degraded closed DCB (CDCB) joints. Good agreement was observed between the FE predictions and the experimental fracture toughness values, when both ODCB and CDBC were aged in the same temperature and humidity conditions. It was also shown that at a given temperature, predictions can be made with reasonable accuracy by extending the knowledge of degradation behavior from one humidity level to another.     

Analysis of a castable refractory using the wedge splitting test and cohesive zone model

A cohesive zone approach is applied to the wedge splitting test (WST) using the finite element code Abaqus to obtain the tensile strength, the fracture energy and insight about the crack wake region. A finite element model updating (FEMU) method, with a cost function based on the measured load (FEMU-F), is used to calibrate the sought parameters. Digital image correlation (DIC) provided the kinematic boundary conditions, and the images were also used to define the geometry for the finite element analysis. Besides the fracture energy analysis and the experimental load, gray level images and displacement fields are analyzed in order to validate the results. The cohesive region is active in the whole analyzed test as confirmed by estimates using the cohesive length.     

Analysis of the cohesive zone and crack length correction in the adhesively bonded double cantilever beam specimen

The double cantilever beam specimen has been increasingly employed to enable the development of cohesive zone models for adhesive joints. Evaluation of the traction–separation law (TSL) requires elaborate experimental techniques and usually relies on data measured until the crack initiation point. Nonetheless, current standards stipulate fracture energy measurements under steady-state crack propagation. This paper investigated the influence of the cohesive zone on the commonly used corrected beam theory data reduction scheme. Analytical solutions for the elastic–perfectly plastic, bilinear, and trapezoidal laws were developed using a beam model. The role of the elastic traction decay zone was found to be significant for high strength moderately tough adhesives. Nevertheless, the results showed that the sensitivity of the crack length correction to the cohesive zone can be exploited to obtain approximate TSLs.     

Prediction of mechanical behaviour of adhesively bonded CFRP scarf jointed specimen under tensile loading using localised DIC and CZM

The present study focuses on the mechanical behaviour of both single and double tapered scarf adhesively bonded joint of Carbon fibre reinforced polymer (CFRP) laminate as adherend subjected to tensile loading. The layup sequence of the CFRP adherend having unidirectional (UD) [0⁰]₁₆ and quasi [+45/−45/0/90]_2S are studied. The adhesive used here is Araldite 2015 supplied by Huntsman which is a two part epoxy system of intermediate toughness grade. Here, 2D digital image correlation (DIC) technique is used for capturing the whole field longitudinal, peel and shear strain distribution over the adhesive bond line of the CFRP specimen. Further, a localised DIC measurement is also carried out using microscopic tube lens for precisely capturing strain field over concentrated zones where damage initiation occurs. The evolution of whole field strain distribution with increasing load is captured to predict the mechanical behaviour and failure mechanism of a tapered scarf joint specimen. In addition, 2-D finite element analysis (FEA) of scarf joint model is carried out for validating the DIC results. In the finite element model cohesive zone elements are used for the modelling of both adhesive layer and inter/intra laminar interface of the composite laminate. Initially, to verify the proposed numerical model, joint's initial stiffness, failure load and corresponding displacement obtained from FEA are compared against the experimental load – displacement results. Later, qualitative and quantitative comparison of longitudinal, peel and shear strain values obtained over the adhesive layer by DIC and FEA is carried out to confirm the accuracy of the DIC results. A decent correlation is found to exist between the DIC predictions and numerical results thereby confirming the accuracy of the DIC technique. Analytical solutions are also derived for the same problem based on mechanics of material and further it is compared with both FEA and DIC predictions for completeness.     

Numerical and experimental analysis of bonded joints with combined loading

The metallic materials bonding using structural adhesives has become an increasingly used process, presenting advantages when compared to other fastening methods such as screws and rivets. The aim of this paper is the numerical evaluation of bonded joints with combined loading (traction and shear) using the finite element method, comparing the results obtained with the experiments performed at the same configurations. Considering adhesive joints with the same bonded area, but with different linear dimensions, the mechanical strength may be different, which characterizes the shape factor. In this way, the analyzes considered the bonded area shape factor in nine different configurations, being modified both the height and the width of the joint, considering two points of force application for each group. For the numerical simulation, the cohesive zone models (CZM) were used, which use the concepts of linear elastic fracture mechanics (LEFM). These models consider that one or multiple interfaces or regions of fracture may be artificially introduced into the structures, which is done through the separation-traction laws. For this purpose, DCB (double cantilever beam) and ENF (end notched flexure) tests were performed, measuring this way the essential cohesive properties to the numerical modeling, especially the critical energy release in I and II modes (normal and shear, respectively). The influence of some cohesive properties on the maximum load of the bonded joint was investigated. The good numerical and experimental concordance in different configurations studied confirms that the CZM provide consistent results with the bonded joint experiments for the presented conditions of adhesive thickness, surface treatment and load application point, not only in single lap joints, but also in combined loading joints, whose investigation was done in this work.